Time continuous FIR filter to implement a hilbert transform and corresponding filtering method

ABSTRACT

A finite impulse response (FIR) filter for implementing a Hilbert transform is provided. The FIR filter includes a plurality of programmable delay cells connected in cascade between an input terminal of the FIR filter and an output terminal of the FIR filter. Each programmable delay cell has associated therewith a constant filter coefficient and a programmable delay coefficient. The FIR filter is also applicable for processing signals originated by the reading of data from a magnetic storage media which employs perpendicular recording.

FIELD OF THE INVENTION

[0001] The preset invention relates to a time-continuous finite impulse response (FIR) filter for implementing a Hilbert transform, and to a method of filtering signals whose spectrum are unknown a priori. That is, the spectrum of the signals are not known before being filtered. In particular, the present invention relates to a circuit structure for programmable time-continuous analog filters specifically intended for read/write operations from/into magnetic storage media.

BACKGROUND OF THE INVENTION

[0002] A circuit structure designed to implement a Hilbert transform has a time-continuous FIR (Finite Impulse Response) filter for its basic component, as readily understood by one skilled in the art. More particularly, a Hilbert transform is essentially a constant module 90° phase shifter. This characteristic can be implemented by an impulsive response FIR filter as illustrated in FIG. 5, for example. The frequency response of such a FIR filter can better approach an ideal response by increasing the filter length. The accompanying FIG. 1 shows schematically a conventional FIR filter which includes a plurality of delay cells cascade connected together between an input terminal and an output terminal.

[0003] A distinguishing feature of the cells is that they carry the same amount of time delay, designated Td. The signal output from each cell is then multiplied by a predetermined coefficient c0, . . . ,cn. The summation of all the signals, each multiplied by a respective one of the coefficients c0, . . . ,cn gives a value Y representing the impulse response of the filter.

[0004] The performance of a time-continuous FIR filter is also linked to another parameter, that is, the bandwidth of the signal being input to the chain of the delay cells. The greater the bandwidth, the larger becomes the number of the FIR filter coefficients required for a closer approach to the ideal Hilbert transform.

[0005] It is a recognized fact that the frequency response of an amplified signal amplitude is related to the frequency response of the signal phase. As the input signal bandwidth grows wider, the phase frequency response becomes smaller, and the so-called group delay is reduced. In fact, the group delay is the derivative of the phase with respect to frequency.

[0006] In other words, with an input signal having a broad bandwidth, a FIR filter with a very large number of coefficients must be used to obtain a desired frequency response. However, this requires fairly complicated and expensive circuit structures, and a demanding one in terms of circuit area.

[0007] Furthermore, where the input signal has different spectrum forms, there are no circuit structures available which can handle the frequency response in an optimum manner. It is customary in such cases to adopt either of two different approaches.

[0008] A first approach employs a FIR filter which has a fixed number of coefficients c0, . . . ,cn so that the filter performances are those as desired for all the spectrum inputs. A second approach uses a filter having coefficients c0, . . . ,cn which can be programmed to fit the spectrum of the input signal.

[0009] The first approach obviously involves a larger number of elements than the second approach. However, the basic element in the first approach is that it is simpler to construct on account of the coefficients being non-programmable. While being advantageous from several aspects and substantially meeting current requirements, neither the first nor the second of the above approaches fill all the demands of processing input signals whose spectrum is unknown a priori.

SUMMARY OF THE INVENTION

[0010] The technical problem underlying the present invention is to provide a FIR filter design for implementing a Hilbert transform, which has appropriate structural and functional features to enable processing of signals whose spectrum are unknown beforehand, thereby overcoming the limitations and drawbacks of prior art designs.

[0011] The principle behind the present invention is to use a FIR filter with constant coefficients, and optimizing the filter response for the input signal spectrum by modifying the time delay of the cells.

[0012] Based on this principle, the technical problem is solved by a filter as previously indicated and defined in claims 1 and following.

[0013] The technical problem is further solved by a filtering method for processing signals having spectrum unknown beforehand, as defined in claims 5 and following.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The features and advantages of a filter and filtering method according to the invention will be apparent from the following description of preferred embodiments thereof, given by way of a non-limitative example with reference to the accompanying drawings.

[0015]FIG. 1 shows schematically a conventional FIR filter structure according to the prior art;

[0016]FIG. 2 is a block diagram of a PRLM decoding arrangement according to the prior art;

[0017]FIG. 3 is a block diagram of a PRLM decoding arrangement according to the present invention;

[0018]FIG. 4 shows comparative plots of response vs. time, respectively, for longitudinal recording and perpendicular recording signals relating to the reading of data from magnetic storage media according to the prior art;

[0019]FIG. 5 is a plot of response vs. time for a Hilbert FIR filter according to the prior art;

[0020]FIGS. 6A and 6B are respective plots of frequency response for components of the decoding arrangement shown in FIG. 4;

[0021]FIGS. 7A, 7B and 7C are respective plots of frequency response for the Hilbert FIR filter according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] Referring to the drawings, and in particular to the example of FIG. 3, the block structure of a Hilbert transform according to the present invention is generally shown at 1 in schematic form. One possible application of the invention concerns the method of recording logic information in magnetic storage media, such as hard disks, for example.

[0023] In particular, an object of the present invention is to increase storage density by allowing the logic information to be recorded in the magnetic storage medium along a vertical direction. This recording method is known as “perpendicular recording” and affords increased storage density for a given area of the magnetic storage medium over “longitudinal recording”. Longitudinal recording is the type of magnetization currently in use. Perpendicular recording effectively enhances the storage density of information in magnetic media, such as hard disks.

[0024] To decode a signal from longitudinal recording, a decoding arrangement of the Partial Response with Maximum Likelyhood type, shown schematically in FIG. 2, is usually employed. A first block VGA is a voltage gain amplifier which is input a signal from a device arranged to read data from a magnetic storage medium, which is not shown because it is conventional.

[0025] Connected to the output of the block VGA is a low-pass filter LPF having an analog-to-digital converter ADC placed downstream of it. An equalizer eqFIR is connected to the output of the converter ADC. The arrangement shown in FIG. 2 can be advantageously modified for processing and decoding signals from perpendicular recording.

[0026] On account of the properties of the Hilbert transform, the output signal from a Hilbert filter FIR is quite similar to the input signal to the low-pass filter LPF of FIG. 2. Accordingly, the same decoding arrangement used for longitudinal recording can be used for perpendicular recording if a Hilbert filter FIR is connected in the block chain.

[0027] More particularly, as shown in the example of FIG. 3, the Hilbert filter FIR is connected between the block VGA and the low-pass filter LPF. Plotted in FIG. 4 is an impulse response relating to two different magnetizations originating from a positive isolated transition, a double transition (d-pulse), and a negative isolated transition.

[0028] With the decoding arrangement illustrated in FIG. 3, the signal indicated by a solid line in FIG. 4 relate to perpendicular recording and can be converted to a signal as indicated by the dashed line, which is representative of longitudinal recording. The transfer function provided by the invention is aimed at minimizing the number of coefficients of the Hilbert FIR by imposing a 90° phase shift in the range of interest, but accepting a substantially non-constant module.

[0029] In essence, to recover a gain variation, particularly a gain attenuation, obtaining an increase in gain from another portion of the decoding arrangement was considered. For this purpose, the designs of the low-pass filter LPF and the equalizer eqFIR of FIG. 3 have been altered with respect to an ideal Hilbert filter to compensate for the less-than-ideal performance of the near-Hilbert filter.

[0030] Reference is now made to the graph in FIG. 6A, which shows a curve 3 relating to the transfer function of the low-pass filter, a curve 4 for the equalizer function, and a curve 5 for the Hilbert filter FIR. With this approach the value of the coefficients of the filter FIR, which reproduce the Hilbert transform, becomes a function of the input signal spectrum. This spectrum is dependent on the stored data packing density.

[0031] Thus, the values of FIR would have to be modified according to the more or less inwardly located track of the magnetic storage medium which contains the information to be read, since the density of the stored information and with it the signal spectrum is dependent on which track is being read. Advantageously, this invention provides instead for a modification of the delay value Td of the cells which comprise the filter.

[0032] Td is the value of the delay element of each cell in the time-continuous filter FIR. As can be appreciated from FIGS. 7B and 7C, to program the delay value Td is to program the values of the coefficients c0, . . . ,cn of the time-continuous filter FIR. In these figures, Tc is the inverse channel period of the operating frequency fc, which changes with the position of the read/write head on the magnetic storage medium.

[0033] Thus, according to the invention, a FIR with fixed coefficients can be used, and use can be made of the programmed delay Td=k*Tc to obtain a desired frequency response according to the different storage densities. Plotted in FIG. 7A is the transfer function of a Hilbert transform approximated for three different storage densities.

[0034] It will be appreciated from the foregoing that the filter and filtering method of this invention have a major advantage in that they allow data to be read from magnetic storage media used in the perpendicular recording mode, at the expense of only minor modifications in current apparatus for reading information from such magnetic storage media. 

That which is claimed is:
 1. A time-continue FIR (Finite Impulse Response) filter structure for implementing a Hilbert transform, of the type including a cascade of delay cells connected between an input terminal of the filter and an output terminal, characterized by having constant filter coefficients (c0, . . . ,cn) and a programmable time delay (Td) of the programmable filter cells.
 2. A filter structure according to claim 1 , characterized in that the length of said coefficients (c0, . . . ,cn) is comparable to that of programmable coefficients.
 3. A filter structure according to claim 1 , characterized by being connected in a PRML decoding arrangement.
 4. A filter structure according to claim 1 , characterized in that said delay (Td) is programmable for each cell.
 5. A method of filtering signals whose spectra are unknown a priori, of the type comprising the sequential steps of processing the signal through amplification, low-pass filtering, analog-to-digital conversion, and equalization, characterized in that a step of processing the signal through a Hilbert FIR filter is carried out between the amplifying and low-pass filtering steps.
 6. A method according to claim 5 , characterized in that said Hilbert FIR filter comprises a cascade of delay cells being connected between an input terminal of the filter and an output terminal and having a time delay (Td) which can be programmed to suit the spectrum of the input signal.
 7. A method according to claim 6 , characterized in that said time delay (Td) is related to a channel period (Tc) being the inverse of the working frequency (fc) according to a variable (k), itself a function of the input signal spectrum.
 8. A method according to claim 5 , characterized in that said Hilbert FIR filter has constant filter coefficients (c0, . . . ,cn).
 9. A method according to claim 5 , characterized in that said sequential signal processing is a PRML type of processing. 